3.0 PFC Inductor Considerations

In chapter 2, you created an inductor design for a synchronous DC/DC Buck converter. In
this section of the tutorial, you will learn how to properly simulate and post-process
in MDM an inductor used in an AC/DC converter - a PFC rectifier operating in critical
conduction mode (CCM).

In this topic:

Key Concepts

This topic addresses the following key concepts:

You must accurately set the fundamental frequency and wave shape for MDM
post-processing to obtain correct inductor loss results.

You must take care to determine whether the inductor waveforms are purely
piecewise-linear (PWL), purely sinusoidal, or a mixture of sinusoidal and PWL,
and also whether the sinusoidal component is rectified.

Using more than one steady-state cycle for post-processing will provide the same
results as using just one cycle, but will take longer.

Post-processing takes longer when the waveforms are more complex.

Just because an AC/DC converter is connected to the AC line voltage does not
necessarily mean that the full line cycle is the inductor waveform steady-state
cycle.

It is your responsibility to ensure that the converter is in steady-state when
you are running a transient simulation instead of a POP analysis.

What You Will Learn

In this topic, you will learn the following:

What are the different types of wave shapes that MDM can recognize.

How to properly set up MDM post-processing for an inductor of a PFC
rectifier.

3.1 PFC Circuit and Inductor

Open the schematic 3.0_PFC_Critical_Conduction_Mode_with_MDM_Inductor.sxsch
which is provided in the zip archive of examples you downloaded at the beginning of
this tutorial. You will see the following circuit:

In this tutorial, you will focus on the inductor design for the PFC converter. The
inductor design has already been provided and you will not modify it. The focus is
only on correctly identifying the inductor fundamental frequency and wave shape of
the inductor in order to properly set up and perform MDM post-processing.

You will notice in the above schematic that inductor L2 has been marked for
MDM post-processing and therefore contains a Level 2 model. Double click the symbol
L2.

3.2 Waveform Shapes Recognized by MDM

Double-click L2 to re-open the Edit Multi-Level PWL Inductor
dialog.

Click on the down arrow in the Wave shape drop-down menu. You will see the
following waveform shapes that you can select:

Piecewise linear (PWL): use this when the inductor (or transformer)
voltage, current, and flux density waveforms consist entirely of linear
segments. You used this wave shape in the previous chapter for the Buck
converter. This shape is typically encountered in non-resonant DC/DC converters
(Buck, Boost, Buck-Boost, SEPIC, Ćuk, etc.).

Sinusoidal (One or more frequencies): use this when the waveforms consist
of several sinusoids imposed on one another, or if they are just a single ideal
sinusoid. You will typically encounter such waveforms in EMI filters, resonant
converters and of course many other circuits outside of switching
converters.

Rectified sinusoidal (Ideal): a single rectified sinusoid. Encountered
for example as the output of a diode rectifier.

Sinusoidal with PWL HF ripple: use this when the waveform has a lower
frequency sinusoidal carrier (e.g. 50-100Hz) upon which a higher PWL switching
waveform (e.g. in the kHz range) is superimposed. A type of waveform found in
many AC/DC, DC/AC, and AC/AC converters.

Rectified sinusoidal with PWL HF ripple: same as above, but with the
sinusoidal carrier rectified. Found in many AC/DC converters.

What if your waveform does not neatly fit into any of the above categories? In that
case, use Sinusoidal (One or more frequencies) as the fallback setting, as
any waveform can be represented as a series of sinusoidal harmonics. You could have
used that setting for example for the Buck converter in the previous chapter,
instead of the PWL setting, but the core losses calculated would have been
considerably less accurate.

3.3 Determine the Inductor Waveform Shape and Frequency

Uncheck the Power probe calculates detailed losses... checkbox. You do
NOT want to run MDM post-processing immediately. First you have to determine the
fundamental frequency and wave shape. To do this you will initially run the
simulation without post-processing. Click OK to close the dialog:

Press F9 to run the simulation. You will notice that this schematic is set up
to perform a Transient analysis rather than the POP analysis that you
performed in the previous chapter. When running a transient analysis, it is your
responsibility to make sure that the simulation lasts long enough for the circuit to
settle into steady-state.

When the simulation finishes, select the simplis_tran1 Vout tab at the bottom
of the Waveform Viewer. You will see that the inductor current (green) has settled
into steady-state by the end of the simulation:

Now zoom in on the inductor current around a zero-crossing. Clearly you can see that
the inductor current is a rectified sinusoidal waveform, with higher frequency PWL
ripple:

You can see that a PWL, high-frequency switching ripple is super-imposed on the
sinusoidal carrier wave. Since the PFC rectifier is running in critical conduction
mode, the current always decreases to zero before the next conversion cycle
begins.

The AC line in this schematic has a frequency of 50Hz. Therefore you could set
the fundamental frequency of the waveform as 50Hz - this would not be wrong.
However, since the sine wave line voltage is rectified, the first and second half of
the line cycle are the same as far as the inductor waveforms are concerned. Using
50Hz would produce correct results, but would needless repeat the same calculations
twice. So, in this case, 100Hz can be used as the fundamental frequency.

To set now the schematic for MDM post-processing:

Double-click the symbol L2.

In the resulting dialog, check the Power probe calculates detailed
losses... checkbox.

3.4 Run the Simulation and MDM Post-Processing

Press F9 to run the simulation. You will notice that MDM post-processing takes
significantly longer than it took with the Buck converter. The pop-up dialog showing
that MDM post-processing is in progress, may, depending on the speed of your
machine, be displayed for about a minute:

Finally the MDM Results window will appear:

Switch to the Waveforms tab of the results window:

If you zoom in the flux density waveform you will see the PWL ripple:

In order to accurately calculate core losses, MDM calculates the energy loss for each
of these PWL flux segments and then averages the total over the 100Hz period to
calculate the average power loss for the entire waveform. This is why the
post-processing takes significantly longer than in the Buck converter, where the
flux density waveform contains only two PWL segments. Therefore, the more complex
and larger the waveform, the longer the post-processing will take.

You can now close this schematic and the MDM Results window. This concludes the
treatment of inductors in this tutorial. You will now move to transformer design in
the next chapter: 4.0 Flyback Converter Transformer Design